It was the home side that took the lead after 16 minutes, however, when Ricardo Vaz Te headed home from close range.
West Ham were back ahead in the early stages of the second period when Mohamed Diame curled an effort into the back of the net.
However, United fought back once more as Robin van Persie turned home from close range after Kagawa had struck the post late on.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
WEST HAM: Jaaskelainen; Demel, Collins, Reid, O’Brien; Diame, O’Neil; Vaz Te, Nolan, Jarvis; Carroll
MANCHESTER UNITED: De Gea; Rafael, Ferdinand, Vidic, Evra; Valencia, Carrick, Jones, Kagawa; Rooney, Van Persie